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C9×Dic11×C47 #32915893

order18612
automorphism?
homologyAbelianization (H1) = C4×C9×C47 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic11×C47
unambiguous semidirect productC11⋊(C4×C9×C47)

Splittings

derived, SylowC11 ⋊ C4×C9×C47
HallC9×C11×C47 ⋊ C4
HallC11×C47 ⋊ C4×C9
HallC9×C11 ⋊ C4×C47

Subgroups

subgroupG/H
center, hypercenterC2×C9×C47D11
commutator, hypocenterC11C4×C9×C47
FrattiniC2×C3C3×D11×C47
FittingC2×C9×C11×C47C2
socle, prime radicalC2×C3×C11×C47C2×C3
cosocleC2×C3×C11C2×C3×C47
LCSG ▷ C11
UCSC1 ◁ C2×C9×C47

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18612

Conjugacy classes & character table

5922 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18612, 3);